Flying to France or Japan? The rules are basically the same: straighteners are allowed. However, voltage differences are the real villain here. Your U.S. straightener will fry itself in a 220-volt European outlet without a converter—and I mean fry, like a tiny electric funeral. Bring a power adapter and a voltage converter, unless you want to buy a new straightener in a Parisian pharmacy.
Also, some countries, like India or the UAE, have stricter rules on battery-powered devices. A quick Google search of your destination’s civil aviation authority is your best friend. Or just pack your old-fashioned plug-in one and call it a day.